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In a beauty contest, half the number of experts voted Mr. A and two thirds voted for Mr. B 10 voted for both and 6 did not for either. How may experts were there in all.

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Let the total number of experts be .

is the set of experts who voted for miss .

is the set of experts who voted for miss .

Since did not vote for either, n.

and

.

So,

Solving the above equation gives

is the set of experts who voted for miss .

is the set of experts who voted for miss .

Since did not vote for either, n.

and

.

So,

Solving the above equation gives

If all the words, with or without meaning, are written using the letters of the word QUEEN add are arranged as in English Dictionary, then the position of the word QUEEN is

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Letters of the word QUEEN are E,E,N,Q,U

Words beginning with E (4!) = 24

Words beginning with N (4!/2!)=12

Words beginning with QE (3!) = 6

Words beginning with QN (3!/2!)= 3

Total words = 24+12+6+9=45

QUEEN is the next word and has rank 46th.

In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every other player. Also, the total number of games played by the men among themselves exceeded by 66 the number of games that the men played against the women. Then the total number of players in the tournament is

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If $\frac{n!}{2!(n-2)!}$ and $\frac{n!}{4!(n-4)!}$ are in the ratio 2:1, then the value of n is

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A polygon has 44 diagonals, the number of sides are

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9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is

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So Ans is [(6C5)5!](4!) = 6!4! = 17280

A student council has 10 members. From this one President, one Vice-President, one Secretary, one Joint-Secretary and two Executive Committee members have to be elected. In how many ways this can be done?

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How many natural numbers smaller than can be formed using the digits 1 and 2 only?

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If n is an integer between 0 to 21, then find a value of n for which the value of $n!(21-n)!$ is minimum

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m distinct animals of a circus have to be placed in m cages, one is each cage. There are n small
cages and p large animal (n < p < m). The large animals are so large that they do not fit in small
cage. However, small animals can be put in any cage. The number of putting the animals into
cage is

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Let A and B two sets containing four and two elements respectively. The number of subsets of
the A × B, each having at least three elements is

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n(B) = 2

Then the number of subsets in A*B is 2^{8 }= 256

If , then the values of n and r
are:

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There are 50 questions in a paper. Find the number of ways in which a student can attempt one or more questions :

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How many words can be formed starting with letter
D taking all letters from the word DELHI so that the
letters are not repeated:

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Naresh has 10 friends, and he wants to invite 6 of
them to a party. How many times will 3 particular
friends never attend the party?

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There is a young boy’s birthday party in which 3
friends have attended. The mother has arranged 10
games where a prize is awarded for a winning game.
The prizes are identical. If each of the 4 children
receives at least one prize, then how many
distributions of prizes are possible?

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In an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is

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